Angular Momentum problem v2 (mass moving inward or outward)

[losbellos]

TL;DR Summary

An other angular momentum problem, code included that runs in a browser. Press F12 for more info.

Hello, simplified the Angular momentum problem that comes up when i try to solve a mass moving inward or outwards and it does not conserver the angular momentum properly. I have tried this is many software by now, or by someone else and we all have found that there is no angular momentum conservation that can be called valid.

So I wrote some equations and try to write my onw solver but could not solve for a valid force (or torque) that would accelerate and decelerate considering the mass differences (frame and moving in mass), location, time, accel etc...

I wonder anyone can present a simple code that can actually prove that angular momentum conservation valid in a simple case.. I'd say two point is good enough...Here is my code have a look at it if you like.
Also please advise if you ever used any software and was validated that in simple problems like this conserves the angular momentum...

https://files.fm/u/zgjafqaxa

 

[hutchphd]

TL;DR Summary: An other angular momentum problem, code included that runs in a browser.

I wonder anyone can present a simple code that can actually prove that angular momentum conservation valid in a simple case..

See Feynman I 18-3.

 

[Ibix]

OP don't seem to include any code so I don't know if this is your problem, but some types of numerical integrators are well known for producing simulations that don't respect conservation laws. The problem is in their methods of approximate integration, not the underlying theory.

 

[losbellos]

OP don't seem to include any code so I don't know if this is your problem, but some types of numerical integrators are well known for producing simulations that don't respect conservation laws. The problem is in their methods of approximate integration, not the underlying theory.

Its up now again, sorry I did not see that after edit, it was lost for the edit post page.

 

[losbellos]

Made an other equation to try to solve the misery of the moving mass inwards to the center of the rotation and the conserved angular momentum etc

TAM, total angular momentum initial condition's value
ratio, ratio of the radiuses at the actual points (outer rim's radius/current location of the mass in terms of distance aka radius because it is moving inwards on a radius line)
vf, velocity of the outer rim of the frame
vm, velocity of the moving mass
vfp, it is the velocity that needs to be added to the vf
mm, mass of the moving mass
vfo, original velocity of the outer rim of the frame
AMF, original, initial angular momentum of the frame
REFFa, a set reference acceleration like 0.0001
rm, current location of the mass
TQF, Torque required to accelerate the frame with reference acceleration
TQM, Torque required to accelerate the mass at the current location with reference acceleration

TAM * ratio * (((vf + vfp)/ts/REFFa*TQF)) = ((vf + vfp) / vfo * AMF + (vm - (vm - (vf / ratio + vfp / ratio))) * mm * rm) * ((vf + vfp) / (vm - (vm - (vf / ratio + vfp / ratio))))*((vm - (vm - (vf / ratio + vfp / ratio)))/ts/REFFa*TQM)
ts, timestep
Here is an equation that makes sense it uses the angular momentum and the force(Torque) in order to find a pair of velocities that fullfills the criteries at a specific point on the way inwards the system

Left side of the equation:
Total angular momentum * ratio of the radiuses * (((current vel of the frame(outer rim) + vel to be added)/timestep/referenceA*TQ req for ref a for the frame))
Try to understand that these values must match on the right side too but by different phenomenon. For example as much force used to accel the frame as much will be used to decel the mass... so it is very useful.
I know that it seems that the left side doesn't make sense but the values are multiplying together in order to make a result that only can be if the right side also multiples these values together and since they are produced in a progress moving inwards the variations that maybe producing the same result and not producing invalid ratio of the velocities, torque etc are totally zero...

Right side:
total angular momentum * ratio of the velocities * Torque required to decelerate the masses

total angular momentum
((vf + vfp) / vfo * AMF + (vm - (vm - (vf / ratio + vfp / ratio))) * mm * rm)
Ratio of the velocities
((vf + vfp) / (vm - (vm - (vf / ratio + vfp / ratio))))
Torque Required to decelerate the mass (Must be the same for the frame)
((vm - (vm - (vf / ratio + vfp / ratio)))/ts/REFFa*TQM)

So this way the result produces velocities that are conserving the angular momentum and using the same force to accel decel and keep the system very valid because it cares about the velocities of the masses and their retios related to their locations etc. There is at least 7 criteria's that are in this equation that tries to estimate the valid velocities at the current locations based on what they should have at the new locations and what velocities they had at the previous locations.
So the equation is not sensitive to the inwards velocity, the time step size, but it is unable to deal with insanely dense like 30000 kg/m^3 objects because the equation is only valid if certain values multiplies together doest equals to zero etc... But not too many...

 

[Juanda]

Do you have a drawing of what you're trying to solve?

I'm with @Ibix anyways. If the equations are right but you're seeing energy is not being conserved it can be typically solved by reducing the step size in the simulation.
For example, I wrote some code to calculate the movement of a mass attached to a spring with some friction with the ground.
$$m\ddot{x} = -kx - \textup{sign}\left (\dot{x}\right ) \mu N$$

If I make the friction coefficient $\mu = 0$ then the energy of the system should look like this:

You can see how the potential energy in the spring and kinetic energy in the mass balance each other to keep the total energy in the system constant.However, if the step size is not small enough, then the energy is not conserved.

I can't remember exactly but I believe every time I have seen it happening energy is not conserved because it gets lost. I don't think I have ever seen the opposite where energy is created. It's not relevant to the point I'm trying to make but it's something I've always felt curious about. Maybe it's just related to the iteration process I use for the calculations.